Question

Bella is 23 years old and wants to invest money for her retirement. She wants to have $2,000,000 saved up when she retires at age 65. a) If she can earn 10% per year in an equity mutual fund, calculate the amount of money she would have to invest in equal annual amounts to achieve her retirement goal. be) Alternatively, how much would she have to invest in equal monthly amounts starting at the end of the current year or month respectively. c) Looking at these numbers, most people would think this is affordable. Why do you think most Americans are not saving for their retirement

Answer 1

A) If Bella contributes 3,719.98 per year during 42 years it will get 2,000,000

B) 258.25 if the payment are monthly

C) Because, the retirement is a long-run reward while spending the income in the younger years may be seens as better deal for most americans n my humble opinion.

Step-by-step explanation:

we will calculate which annuity will equal a future value 2,000,000 at 10% in the period of time from 23 years to 65 years:

`FV / ((1+r)^(time) -1)/(rate) = C\\`

PV $2,000,000.00

time 42 (65 years - 23 years )

rate 10% = 10/100 = 0.1

`2000000 * ((1+0.1)^(42) -1)/(0.1) = C\\`

C $ 3,719.98

If Bella contributes 3,719.98 per year during 42 years it will get 2,000,000

IF the payment are monthly, we will increase time and adjust the rate:

`PV / (1-(1+r)^(-time) )/(rate) = C\\`

PV $2,000,000.00

time 504 (42 years x 12 months per year)

rate 0.008333333 (0.1 / 12 months per year)

`2000000 * (1-(1+0.008333)^(-504) )/(0.008333) = C\\`

C $ 258.25